Harnack inequalities, Kobayashi distances and holomorphic motions
Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 206-218.

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We prove some generalizations and analogs of the Harnack inequalities for pluriharmonic, holomorphic and “almost holomorphic” functions. The results are applied to proving smoothness properties of holomorphic motions over almost complex manifolds.
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     title = {Harnack inequalities, {Kobayashi} distances and holomorphic motions},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_279_a12/}
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E. M. Chirka. Harnack inequalities, Kobayashi distances and holomorphic motions. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 206-218. http://geodesic.mathdoc.fr/item/TRSPY_2012_279_a12/

[1] Agard S., Distortion theorems for quasiconformal mappings, Ann. Acad. sci. Fenn. A. I. No 413, 1968, 11 pp. | MR | Zbl

[2] Ahlfors L. V., Conformal invariants: Topics in geometric function theory, AMS Chelsea Publ., Providence, RI, 2010 | MR | Zbl

[3] Alfors L., Lektsii po kvazikonformnym otobrazheniyam, Mir, M., 1969 | MR

[4] Gardiner F. P., Jiang Y., Wang Z., “Holomorphic motions and related topics”, Geometry of Riemann surfaces, LMS Lect. Note Ser., 368, Cambridge Univ. Press, Cambridge, 2010, 156–193 ; arXiv: 0802.2111[math.CV] | MR | Zbl

[5] Kheiman U., Kennedi P., Subgarmonicheskie funktsii, Mir, M., 1980

[6] Hempel J. A., “The Poincaré metric on the twice punctured plane and the theorems of Landau and Schottky”, J. London Math. Soc. Ser. 2, 20 (1979), 435–445 | DOI | MR | Zbl

[7] Jenkins J. A., “On explicit bounds in Schottky's theorem”, Can. J. Math., 7 (1955), 76–82 | DOI | MR | Zbl

[8] Kobayashi S., Hyperbolic manifolds and holomorphic mappings, M. Decker, New York, 1970 | MR

[9] Lehto O., Virtanen K. I., On the existence of quasiconformal mappings with prescribed complex dilatation, Ann. Acad. sci. Fenn. A. I. No 274, 1960, 24 pp. | MR | Zbl

[10] Mañé R., Sad P., Sullivan D., “On the dynamics of rational maps”, Ann. sci. Éc. Norm. Supér. Sér. 4, 16 (1983), 193–217 | MR | Zbl

[11] Nehari Z., Conformal mapping, Dover Publ., New York, 1975 | MR

[12] Royden H. L., “Remarks on the Kobayashi metric”, Several complex variables, Proc. Conf. (Univ. Maryland, 1970), v. II, Lect. Notes Math., 185, Springer, Berlin, 1971, 125–137 | DOI | MR

[13] Royden H. L., “The extension of regular holomorphic maps”, Proc. Amer. Math. Soc., 43 (1974), 306–310 | DOI | MR | Zbl

[14] Vekua I. N., Obobschennye analiticheskie funktsii, Nauka, M., 1988 | MR | Zbl